Regularity criteria for the topology of algebraic curves and surfaces

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 4647 LNCS, Issue , 2007, Pages 1-28

  Alberti, Lionel ^a   Mourrain, Bernard ^a  

^a INRIA   (France)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION ALGORITHMS; BOUNDARY CONDITIONS; NUMERICAL METHODS; POLYNOMIAL APPROXIMATION; TOPOLOGY;

ALGEBRAIC CURVES; LOCAL CONIC STRUCTURE; POLYNOMIAL EQUATIONS; SINGULAR POINTS;

LINEAR ALGEBRA;

EID: 38049058756     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-73843-5_1     Document Type: Conference Paper

References (44)

1. Bloomenthal, J.: Introduction to implicit surfaces. Morgan Kaufmann, San Francisco (1997)
2. Grandine, TA., Klein, F.W.: A new approach to the surface intersection problem. Computer Aided Geometric Design 14, 111-134 (1997)
3. Farin, G.: An ssi bibliography. In: Geometry Processing for Design and Manufacturing, pp. 205-207. SIAM, Philadelphia (1992)
4. Kalra, D., Barr, A.: Guaranteed ray intersections with implicit surfaces. In: Proc. of SIGGRAPH, vol. 23, pp. 297-306 (1989)
5. Lorensen, W., Cline, H.: Marching cubes: a high resolution 3d surface construction algorithm. Comput. Graph. 21(4), 163-170 (1987)
6. Zhou, Y., Baoquan, C., Kaufman, A.: Multiresolution tetrahedral framework for visualizing regular volume data. In: Proc. of Visualization '97, pp. 135-142 (1997)
7. Bloomenthal, J.: Polygonization of implicit surfaces. Computer-Aided Geometric Design 5(4), 341-355 (1988)
8. Bloomenthal, J.: An implicit surface polygonizer. In: Heckbert, P. (ed.) Graphics Gems IV, pp. 324-349. Academic Press, Boston, MA (1994)
9. Hartmann, E.: A marching method for the triangulation of surfaces. Visual Computer 14(3), 95-108 (1998)
10. Witkin, A., Heckbert, P.: Using particles to sample and control implicit surface. In: Proc. of SIGGRAPH, pp. 269-277 (1994)
11. Boissonnat, J.D., Oudot, S.: Provably good sampling and meshing of surfaces. Graphical Models 67, 405-451 (2005)
12. Dey, T.K.: Curve and Surface Reconstruction: Algorithms with Mathematical Analysis (Cambridge Monographs on Applied and Computational Mathematics). Cambridge University Press, Cambridge (2006)
13. Collins, G.E.: Quantifier elimination for real closed fields by cylindrical algebraic decomposition. In: Brakhage, H. (ed.) Automata Theory and Formal Languages. LNCS, vol. 33, pp. 134-183. Springer, Heidelberg (1975)
14. Keyser, J., Culver, T., Manocha, D., Krishnan, S.: Efficient and exact manipulation of algebraic points and curves. Computer-Aided Design 32(11), 649-662 (2000)
15. González-Vega, L., Necula, I.: Efficient topology determination of implicitly defined algebraic plane curves. Comput. Aided Geom. Design 19(9), 719-743 (2002)
16. Gatellier, G., Labrouzy, A., Mourrain, B., Tecourt, J.P.: Computing the topology of 3-dimensional algebraic curves. In: Computational Methods for Algebraic Spline Surfaces. LNCS, pp. 27-44. Springer, Heidelberg (2005)
17. Alcázar, J.G., Sendra, J.R.: Computing the topology of real algebraic space curves. J. Symbolic Comput. 39, 719-744 (2005)
18. Fortuna, E., Gianni, P., Parenti, P., Traverso, C.: Computing the topology of real algebraic surfaces. In: ISSAC '02. Proceedings of the 2002 international symposium on Symbolic and algebraic computation, pp. 92-100. ACM Press, New York (2002)
19. Cheng, J.S., Gao, X.S., Li, M.: Determining the topology of real algebraic surfaces. In: Martin, R., Bez, H., Sabin, M.A. (eds.) Mathematics of Surfaces XI. LNCS, vol. 3604, pp. 121-146. Springer, Heidelberg (2005)
20. Mourrain, B., Técourt, J.: Isotopic meshing of a real algebraic surface. Technical Report 5508, INRIA Sophia-Antipolis (2005)
21. Sherbrooke, E.C., Patrikalakis, N.M.: Computation of the solutions of nonlinear polynomial systems. Comput. Aided Geom. Design 10(5), 379-405 (1993)
22. Elber, G., Kim, M.S.: Geometric constraint solver using multivariate rational spline functions. In: Proc. of 6th ACM Symposium on Solid Modelling and Applications, pp. 1-10. ACM Press, New York (2001)
23. Mourrain, B., Pavone, J.P.: Subdivision methods for solving polynomial equations. Technical Report 5658, INRIA Sophia-Antipolis (2005)
24. Sederberg, T.: Algorithm for algebraic curve intersection. Computer Aided Design 21, 547-554 (1989)
25. Hass, J., Farouki, R.T., Han, C.Y., Song, X., Sederberg, T.W.: Guaranteed Consistency of Surface Intersections and Trimmed Surfaces Using a Coupled Topology Resolution and Domain Decomposition Scheme. Advances in Computational Mathematics (to appear)
26. Seong, J.K., Elber, G., Kim, M.S.: Contouring 1- and 2-Manifolds in Arbitrary Dimensions. In: SMI'05, pp. 218-227 (2005)
27. Liang, C., Mourrain, B., Pavone, J.: Subdivision methods for 2d and 3d implicit curves. In: Computational Methods for Algebraic Spline Surfaces, pp. 171-186. Springer, Heidelberg (to appear) also available at http://hal.inria.fr/ inria-00130216
28. Alberti, L., Comte, G., Mourrain, B.: Meshing implicit algebraic surfaces: the smooth case. In: Maehlen, M., Morken, K., Schumaker, L.L. (eds.) Mathematical Methods for Curves and Surfaces: Tromso'04, Nashboro, pp. 11-26 (2005)
29. Farin, G.: Curves and surfaces for computer aided geometric design: a practical guide. Comp, science and sei. computing. Academic Press, Boston, MA (1990)
30. Emiris, I.Z., Mourrain, B., Tsigaridas, E.P.: Real algebraic numbers: Complexity analysis and experimentations. In: Reliable Implementation of Real Number Algorithms: Theory and Practice. LNCS, Springer, Heidelberg (to appear) also available at http://hal.inria.fr/inria-00071370
31. Eigenwillig, A., Sharma, V., Yap, C.K.: Almost tight recursion tree bounds for the descartes method. In: ISSAC '06. Proceedings of the 2006 International Symposium on Symbolic and Algebraic Computation, pp. 71-78. ACM Press, New York (2006)
32. Pavone, J.: Auto-intersection de surfaces pamatrées réelles. PhD thesis, Université de Nice Sophia-Antipolis (2004)
33. Floater, M.S.: On zero curves of bivariate polynomials. Journal Advances in Computational Mathematics 5(1), 399-415 (1996)
34. Abhyankar, S.: Algebraic Geometry for Scientists and Engineers. American Mathematical Society, Providence, R.I. (1990)
35. Walker, R.: Algebraic curves. Springer, Heidelberg (1978)
36. Lloyd, N.G.: Degree theory. Cambridge Tracts in Mathematics, Cambridge University Press, Cambridge No. 73 (1978)
37. Dickenstein, A., Rojas, M.K.R., Shihx, J.: Extremal real algebraic geometry and a-discriminants (preprint)
38. Goresky, R.M.M.: Stratified Morse Theory. Springer, Heidelberg (1988)
39. Whitney, H.: Elementary structure of real algebraic varieties. Annals of Math. 66(2) (1957)
40. Speder, J.P.: Équisingularité et conditions de Whitney. Amer. J. Math. 97(3) (1975)
41. Thom, R.: Ensembles et morphismes stratifiés. Bull. Amer. Math. Soc. 75 (1969)
42. Mather, J.: Notes on topological stability. Harvard University (1970)
43. Eisenbud, D., Huneke, C., Vasconcelos, W.: Direct methods for primary decomposition. Invent. Math. 110, 207-235 (1992)
44. Cox, D., Little, J., O'Shea, D.: Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra. Undergraduate Texts in Mathematics. Springer, Heidelberg (1992)